Literature Review
2.1 MPPT techniques for partial shading effects mitigation
Generally, the MPPT conventional algorithms use one or more electrical parameter references to compare with the system values obtained by the sensors in some of the power system electrical characteristics. In this way, the error of the closed loop con-trol system is computed and the corresponding corrections are done.
In a more complex way, stochastic algorithms use several time steps to create a set of values, or family of values, and apply the algorithm corrections to generate the next family of the value set, until the system reaches the convergence point.
The common point in the whole pack of algorithm types is that they must find the system work MPP and hence achieve the maximum efficiency possible of the whole system.
2.1.1 Deterministic MPPT algorithms
This algorithm category is mainly based on a simple cause-effect principle.In most cases, it uses a two-step measure comparison, basically determining how the system reacts after applying a perturbation into it and finally acting in consequence, according to the algorithm definition.
In general, literature coincides in the fact that this kind of algorithm has an adequate performance in cases where the power curve that represents the PV array configura-tion has a unique maximum or, in other words, where the system can be found in a surrounding where the irradiation is constant and homogeneous in the whole PV panel region.
The next subsections are presenting then, the algorithms that fits better regarding uni-form irradiance condition.
Perturb and observe: Fixed perturbation step
This method, that is based on the trial and error process, measures the actual PV power and then perturbs the operating point by moving the operating voltage at each time cy-cle. From each two time-steps, it monitors the variation of power and actuates in the next perturbation according to this power variation.
2.1. MPPT techniques for partial shading effects mitigation
If the power increases, the next perturbation will follow the same direction or per-turbation sign, whereas if it decreases it shall change the perper-turbation direction. This simple operation is done in a cyclic way until the MPP is reached, that is dP/dV = 0.
Once the tracker reaches the MPP, it oscillates around it, depending this oscillation amplitude on how big the perturbation step is.
Several authors have studied this basic MPPT, sometimes to enhance their weak points as in [4], and sometimes to compare it with other MPPT techniques [5], using the first one as a base reference since it is one of the most usual method applied.
Perturb and observe: Variable perturbation step
This technique proposes substantially the same than the one seen before with the only difference found in the duty step change ratio, which depends on the output reaction to the perturbation. In this way, the duty step ratio is modified according to the next equation,
∆D(n) = α ∗ (P (n) − P (n − 1)) (V (n) − V (n − 1))
where alfa is a weighting parameter, that depends on the PV system model. The sign of this perturbation will follow the same idea, as in the fixed perturbation step.
This variation works appropriately under changing environment since its performance in tracking the MPP is quite fast and the oscillation in the steady-state is low. However, this advantages towards the fixed step Perturb and Observe are compensated with its extra computational load. So it results in a trade-off between accuracy and complexity.
In experimental results, shown in some literature, it is concluded that the proposed algorithm can give significantly faster tracking speed than the conventional P&O method [6].
Perturb and observe: Three weigh point
This method compares three perturbation points instead of two, as in the most com-mon P&O algorithm. It measures the current operating point, A, the next operating point, B after perturbation, and the third one, C, which is double perturbated in op-posite direction and from B reference point. The nine possible different scenarios are
shown in figure 2.1, from author [7], where the status parameter M gains a positive weight if B is equal or greater than A or if A is bigger than C, and it gains a negative weight if B is smaller than A or A is smaller than C.
The final duty cycle change rate will be defined as A, B or C if M is equal to 0, 2 or -2 respectively.
This method has the advantage to avoid the oscillations found in two perturbation P&O and is also considered in literature as a fast tracker method compared to the fixed step P&O.
Figure 2.1: Three weight point scenarios
Perturb and observe: Power curve slope
This method is specially defined into partial shading scenarios. The main core of the Perturb and Observe code is executed while the shading condition is null, therefore in this moment, any type called above of Perturb and Observe technique based program is used, whereas regarding partial shading condition the global peak searching sub-routine part is executed until a criteria condition is achieved.
The searching path is defined through dP/dV sign and the likelihood to start a new global peak tracking depends on the best power peak tracked in a defined period of time. As soon as the new power tracked surpasses the hypothetical local power peak, the algorithm deviates into the conventional Perturb and Observe configuration, doing a normal tracking inside the global peak region. Once the duty cycle reaches the MPP, it oscillates around it, as in the normal case.
This type could be defined as a combined algorithm class, but both routines of the
2.1. MPPT techniques for partial shading effects mitigation
code are done with the Perturb and Observe mechanism basis. In other words, the global peak seeking part is also done as a Perturb and Observe method. Author [8]
proposes this method and tests it.
Incremental Conductance: Fixed perturbation step
Incremental conductance method is based on the MPP found in the power curve that can be computed with the partial derivate of the function respect to the voltage. That is the equation 2.1.
Hence, the position of the working point is defined in the MPP or in the left or the right side of MPP according to the sign of dP/dV . This sign of dP/dV is represented in the equation and inequations seen below:
∆I This technique is also a well know studied method and can be found in several papers. Author [9] proposes an enhanced incremental conductance technique and author [10] makes a comparative study between IC and P&O.
Incremental Conductance: Multi-tracking duty cycle
This modified method is based on the IC main definition but using three tracking par-ticles simultaneously, applying the IC concept. Once all peaks are found, they are compared with a threshold value to discard the local peaks and the global peak duty cycle value is saved.
Therefore, it is a modified method that can be used in both scenarios, with full ir-radiated region and with partial shading.
The drawback of this method is the relative slow tracking of the MPP. Hence, the
correct algorithm part must be used depending on the scenario situation, that is, tun-ing correctly the criteria threshold values that will define the electrical condition found under the diverse shading scenarios which will demand, or not, the global peak seek-ing sub-routine.
This application can be found in [11] where the author proposes and tests in hard-ware this technique.
Fractional Open-Circuit Voltage
This indirect conventional control method uses the widely observed relationship be-tween the PV output voltage at the MPP and the Voc, which are linearly proportional in a full irradiating scenario. The relationship is given in the equation 2.2, where the proportional constant kocdepends on the PV module characteristics, the cell technol-ogy and the climatic conditions. Even though it has several dependences, the constant is usually chosen in a specific case and used for a wide range of climatic conditions.
Therefore, in this method the extracted power is not maximized a priori. Typical val-ues of the constant Vocare between 0,73 and 0,80 with the actual technology used in PV systems.
When the algorithm is operating, it matches the theorical VM P P as the reference volt-age and it refreshes its value each time it reaches a determined number of time steps.
This refreshing is done by calculating the Vocwhich implies to open-circuit the system, with its corresponding loss of power, due to the time that it is disconnected. However, the simplicity of this algorithm implementation makes it viable for an MPP tracking, and even more viable in cases where climatic variations are minimal.
Author [12] proposes this method as a VMPPT in a full irradiation scenario.
VM P P = kocVoc (2.2)
Fractional Short-Circuit Current
In a similar way to the open-circuit voltage tracking, this method uses the observed fact of the linear dependency between the PV current at MPP and the short-circuit cur-rent. Its relationship is also similar to the last method and is shown in the equation 2.3, where the constant ksc is normally considered in a range around 0,85 and it depends on the PV system, the cell technology used and the climatologic conditions once again.
2.1. MPPT techniques for partial shading effects mitigation
It also shares with the last method the negative aspect that causes the Isc value scan-ning, due to the short-circuit of the whole system. While this happens, there is a loss of power which makes it less efficient than other kind of method in this aspect.
Furthermore, it has a constant value that is imposed based on some strict conditions and then, it can not assure its correct accuracy in different climatic conditions which is also a disadvantage in terms of efficiency.
As in the last technique, its simplicity makes it a fair method to implement a MPPT.
With respect to the system parameter changes due to the aging, the short-circuit tech-nique, like in the open-circuit techtech-nique, can overcome easily this problem with low maintenance, since the refreshing aspect of the algorithm uses the true and actual pa-rameters of the system.
Author in [13] proposes and tests this method experimentally.
IM P P = kscIsc (2.3)
Constant Voltage
The constant voltage method is the MPPT control method with the highest level of simplicity. The operating voltage point is compared at each cycle with a constant volt-age reference, making the working point to stay near this match point all the time.
The reference voltage is set as it is done in the open-circuit voltage method but this time there is no control on a linear relationship that depends on some conditions of the PV system. That is, the system is not able to notice a change related to the Voc, which implies a higher error toward changes in an external way but also in an internal way. This last point means that in case of a system deteriorating, with their parameters modification involved, the tracker will still chase an even more wrong point related to a previous parameter state of the system.
It makes this system, on the one hand, the simplest one to realize, but on the other hand, the minimal changes, in the external or internal system, will generate a high loss of accuracy in the tracking issue and, therefore, a high loss of efficiency on the whole system. Due to these points, this kind of method is used to be implemented as a part of a combined tracking system with another method too. In this way, it is used as a fast-early point tracker, leaving the accuracy tracking to the next method once the
working point is close enough to the MPP region.
As in the open-circuit and short-circuit methods, constant voltage method is highly recommended to be used only under full irradiation scenarios.
Author [14] tests this method performance under different irradiation and tempera-ture conditions.
2.1.2 Stochastic MPPT algorithms
Some conventional MPPT algorithms have been described. As in a typical determin-istic algorithm method from this family, they have the enormous advantage of finding a global optimum of the required function. Unfortunately, the multiple local maxima function presents an extra issue to the tracking method, for which this kind of algo-rithm isn’t usually prepared for.
Depending on the situation, the setup configuration and the partial shading condi-tions, a complex power curve shape will be generated, which will contain one or more maxima. Therefore, the previous presented tracking methods, will have a chance to fail in the mission to find and follow the optimal electrical reference that involves the maximum extracted power of the photovoltaic system. If the point selected is not the optimal one, the system can experiment a high decrease of power extracted which, after a several amount of time, implies a low efficiency and a lesser rentability of the inversion.
To overcome this problem, a new type of algorithm is used, the stochastic MPPT algorithm type. This kind of algorithm samples the searching space of the function, exploring the full range of the function solutions instead of doing a sequential explo-ration as in the perturbation and observing method.
Nevertheless, it can not always guarantee the optimal solution, since it is a method that depends in a certain way on the probability and uses pseudo-randomness in its way to find out the global maxima. In the end, it is indeed a fair approach that can increase the chance to hit the correct point and, on average, improve the efficiency.
If it is well designed and implemented, it shall find out most of the time the optimal point that corresponds to the MPP. Of course, it will depend on the type of the power shape too, being some of them more or less easy to be tracked with this kind of MPPT
2.1. MPPT techniques for partial shading effects mitigation
algorithm.
In relation to the stochastic methods, there can be found several types of them which mostly appeared in the recent years due to the wide spread of computers in the last decades. Therefore, until the last 50 years, only deterministic methods were being used.
The high quantity of variants for each type of stochastic algorithm is due to their application focus, that can be completely different depending on the study scenario.
Then, they can be slightly modified to be adapted to a specific case and, consequently, appearing in so many different ways to represent them. However, the main core basis is always the same and normally represents and emulates a natural behaviour easily observed in this world.
In a general point of view, they are usually classified as heuristic or meta-heuristic algorithms, which are learnt with a rule of thumb basis and not following a tough underlying theory. Even though the background theory is quite behind regarding the applicability, their results are fair good.
Particle Swarm Optimization (PSO)
In nature, some species’ behaviour moves around the cooperation to reach a better survival capacity. Generally, in information gathering, they take profit of their own knowledge but also of their group members’ knowledge and the past memory of their own learning and the social or group learning too. This type of social behaviour allows a fast information exchange and an even faster reaction to avoid dangers or to find the best pathing while travelling, for example.
This statement is observed in swarms of animals like in fish schools or flocks of birds, creating that typical ordered and fluent cooperation phenomena that seems to be alive per se. That can be also called emergent phenomena, where the final result of the cooperation activity of several individual particles is completely different to the indi-vidual skills of them (another example seen in nature is the human brain functionality, where single neurons have well-defined and unique purposes, but the activity of the full neural network creates a quite known emergent phenomena, the consciousness).
Taking into account this phenomena, the Particle Swarm Optimization algorithms are
based on the same core ideas, where some particles collaborate as a whole to find the best possible solution to a problem, also known as maxima or minima of an objective function. Each particle, which is a potential solution of the objective function of the problem, knows the position of the best solution ever found by the swarm and of the best solution ever found by itself.
Author in [15] proposes and tests this method with different numbers of particles and compares it with a wide set of MPPT techniques.
Genetic Algorithm (GA)
Also known as evolutionary algorithm (EA) that is based on the evolution theory of Darwin, which exposes, in few words, that the strongest survive and the weakest die, leaving every time a stronger living being more able to survive and to procreate.
In the GA context, this can be compared to the optimization of an objective func-tion as in the previous stochastic algorithm. The power curve is the funcfunc-tion to be tracked and the ‘genes’ are the positions (duty cycle values) attached to a value (chro-mosome). Therefore, the idea of the algorithm is that the strongest genes (closer to maxima or minima) are supposed to survive and procreate, while the weakest just dis-appear. Every crossover of the genes creates a new potential set of solutions that may mutate and hopefully will be better than the previous ones.
This algorithm uses this point iteratively until the genes reach a solution region where is close enough to the maxima, or in other words, they converge into the same gene code which can not get a further enhancement (optima reached).
In citeShaiek2013, the author proposes a GA method and compares it with some con-ventional algorithms.
Ant Colony Optimization (ACO)
This evolutionary algorithm is another nature-inspired algorithm. An ant colony be-haviour with the environment can also be explained with the concept of emergence named before. It uses a group information sharing to define the best possible pathing to find a food source and move it to the ant-hill.
The algorithm ACO based code uses this idea, which basically consist of stigmergy,
2.1. MPPT techniques for partial shading effects mitigation
evaporation and errors. Firstly, the particle integrant of the family group (ant/duty cy-cle value) communicates by leaving global information in its environment (stigmergy) under the form of pheromones (odours) that will evaporate with time. Then, ants check an initial position. If there are no pheromones, they move around randomly. On the other hand, when there are pheromones in the track, ants tend to follow them, propor-tionally depending on the quantity of pheromone concentration that they find in that region of the path. If the ants finds food, they go on walking randomly while leaving a pheromone trail, therefore creating a new track for the next ants. The trails that follow by more than one ant is reinforced (convergence in the optima).
In conclusion, this type of algorithm is robust and has a great adaptability due to
In conclusion, this type of algorithm is robust and has a great adaptability due to